Q. 5 C5.0( 1 Vote )
Solve the following equations :
tan 3x + tan x = 2 tan 2x
Answer :
Ideas required to solve the problem:
The general solution of any trigonometric equation is given as –
• sin x = sin y, implies x = nπ + (– 1)ny, where n ∈ Z.
• cos x = cos y, implies x = 2nπ ± y, where n ∈ Z.
• tan x = tan y, implies x = nπ + y, where n ∈ Z.
given,
tan x + tan 3x = 2tan 2x
⇒ tan x + tan 3x = tan 2x + tan 2x
⇒ tan 3x – tan 2x = tan 2x – tan x
⇒ 
As, tan (A - B) = 
∴ 
⇒ 
⇒ 
∴ tan x = 0 or tan 2x = 0 or tan 3x = tan x
if tan x = tan y, implies x = nπ + y, where n ∈ Z
∴ x = nπ or 2x = mπ or 3x = kπ + x
∴ 
∴ 
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